Finite Group DatabasebetaFinite Group Databasebeta| order | 25530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D851 |
| unambiguous semidirect product | C23⋊(C3×C5×D37) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D851 |
| commutator, cosocle, hypocenter | C23×C37 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C23×C37 | C2 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C3×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12765 |
6405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25530, 5);